A cube of wood and a cube of concrete, each 0.17 m on a side, are placed side by side. One of the long faces of the rectangular prism formed by the two cubes is held at 17°C, and the opposite long face is held at 32°C. What is the total rate of heat transfer through the cubes?
To find the total rate of heat transfer through the cubes, we need to calculate the rate of heat transfer through each cube separately and then add them together.
First, let's calculate the rate of heat transfer through the cube of wood. We'll use the formula for heat conduction:
Q = (k * A * ΔT) / d
Where:
Q is the rate of heat transfer
k is the thermal conductivity of the material (given as 0.08 W/m·°C for wood)
A is the surface area of the cube (given as (0.17)^2 * 6)
ΔT is the temperature difference (given as 32°C - 17°C)
d is the thickness of the cube (given as 0.17)
Using these values in the formula:
Qwood = (0.08 * [(0.17)^2 * 6] * (32 - 17)) / 0.17
Now let's calculate the rate of heat transfer through the cube of concrete. We'll use the same formula with the appropriate values:
Q = (k * A * ΔT) / d
Where:
k is the thermal conductivity of the material (given as 1.2 W/m·°C for concrete)
A is the surface area of the cube (given as (0.17)^2 * 6)
ΔT is the temperature difference (given as 32°C - 17°C)
d is the thickness of the cube (given as 0.17)
Using these values in the formula:
Qconcrete = (1.2 * [(0.17)^2 * 6] * (32 - 17)) / 0.17
Finally, we can find the total rate of heat transfer through the cubes by adding the rates of heat transfer for the wood and concrete:
Qtotal = Qwood + Qconcrete
Now you can substitute the values into these formulas and calculate the total rate of heat transfer through the cubes.